Bagels talks - Spring 2021
| Date | Speaker | Title |
| February 3rd | Yen-An | Log canonical foliation surface singularities
Abstract: Singularities play an important role in many areas of algebraic geometry. One of natural classes of singularities is (log) canonical singularities. These singularities have been extensively studied, especially in the case of surfaces. In particular, we have a full classification of log canonical surface singularities. In this talk, I will give you a full list of log canonical foliation surface singularities. As an application, I will sketch the ascending chain condition for foliated minimal log discrepancies on surfaces. |
| February 10th | Seungsu | Discreteness and rationality of F-jumping numbers in regular rings
Abstract: In this talk, we will prove that the jumping numbers of test ideals are discrete and rational. It is known that test ideals are char p analog of multiplier ideals in char 0. |
| February 17th | You-Cheng | Weighted Gromov-Witten invariants of a point
Abstract: In this talk, I will compute the generating functions of the intersection numbers on Hassett’s moduli of weighted pointed curves and show that they are governed by the KdV integrable hierarchy. If time permitted, I will talk about possible applications to general target spaces. |
| February 24th | Qingyuan | Minimal Model Program for threefolds in positive and mixed
characteristic
Abstract: Miminal Model Program (MMP for short) is a theory aiming at classifying algebraic varieties up to birational equivalence. While MMP in characteristic 0 has been greatly developed over past 40 years, we know relatively little about MMP in positive characteristic, and even less in mixed characteristic. But recently people have made significant progress for MMP in low dimensions. In this talk, after reviewing the basic definitions of MMP and known results in characteristic 0, I will focus on MMP for threefolds in positive and mixed characteristic, and introduce some recent results on that. |
| March 3rd | Jose | Kawamata - Morrison conjecture for Calabi - Yau complete intersection
Abstract: The Kawamata - Morrison conjecture connects the structure of the (birational) automorphism group to the nef (movable) cone. In this talk I will explain how to use Coxeter groups theory to show that the conjecture is true for Calabi - Yau complete intersections given by ample divisors in products of projective spaces. |
| March 10th | No talk |
|
| March 17th | Marin | Stability conditions on projective spaces
Abstract: We study a family of stability conditions on projective space, indexed by a real parameter t. It has been conjectured that for large values of t, the moduli space of semistable objects coincides with the moduli space of Gieseker-semistable sheaves. I will talk about our recent progress on this conjecture. |
| March 24th | Junpeng | Fibrations and birational geometry
Abstract: For elliptic fibrations (algebraic contraction with general fiber elliptic curves), much has been studied well, such as boundedness of minimal models. In this talk, we introduce a new method to get some boundedness results in the higher-dimensional case. |